An extended procedure for finding exact solutions of PDEs arising from potential symmetries

Abstract:
Lie point symmetries and nonlocal symmetries of PDE systems are widely used for construction of exact invariant solutions. I will describe an extended algorithmic procedure that, for a given nonlocal (potential) symmetry, can yield additional exact solutions, which cannot be found using the usual algorithm.
As an example, I will present a tree of nonlocally related PDE systems for planar gas dynamics equations in the Lagrangian framework, a classification of its nonlocal symmetries for a particular constitutive function, and examples of new solutions obtained using the extended algorithm.